The present invention relates to a filter with improved frequency response characteristics. More particularly, the present invention relates to a filter having high gain selectivity and linear phase response characteristics.
The function of a low-pass filter is to pass low frequency analog signals (e.g., from dc to some specified cutoff frequency f.sub.c) and to attenuate higher frequency signals. An ideal low-pass filter would exhibit a perfectly flat response in its passband (i.e., frequencies below f.sub.c) and infinite attenuation in its stopband (i.e., frequencies above f.sub.c), with a rapid transition from passband to stopband. Additionally, it would exhibit "linear" phase characteristics, meaning that the phase shift of an analog signal passing through the filter would increase linearly with linear increases in frequency.
In practice, however, the ideal low-pass filter can only be approximated. For example, the response characteristics of the ideal low-pass filter is often approximated by a ratio of two rational polynomials in the complex frequency domain, in which the highest power of the frequency term in the polynomials determines the "order" of the filter. Increasing the order of the filter generally improves the amplitude response characteristics at the expense of increasing the cost, complexity and number of stages needed to provide such characteristics.
A wide variety of polynomial functions have been employed in filter design. For example, Butterworth, Chebyshev, Legendre and Bessel filters are well-known and used extensively. None of these filters, however, substantially achieve the response characteristics of the ideal low-pass filter.
Such polynomial functions have also been employed in the design of high-pass filters. The ideal high-pass filter would exhibit a perfectly flat response in its passband (i.e., frequencies above f.sub.c) and infinite attenuation in its stopband (i.e., frequencies below f.sub.c), with a rapid transition from passband to stopband. Such an ideal filter also would exhibit linear phase characteristics, in which the phase shift of an analog signal passing through the filter would increase linearly with linear increases in frequency. However, the ideal high-pass filter also has not been achieved.
Such polynomial functions have also been employed in the design of bandpass filters. As is the case with low-pass and high-pass filters, the ideal bandpass filter has also not been achieved.
In view of the foregoing, it would be desirable to provide an efficient and low cost filter with improved frequency response characteristics, more particularly, improved gain selectivity, and substantially linear phase response characteristics.
It would also be desirable to provide such a filter that passes low frequency signals and attenuates higher frequency signals.